%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GEG006^1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:49:18 AM UTC 2026
% Result : Theorem 2.77s 0.71s
% Output : CNFRefutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 12
% Syntax : Number of formulae : 118 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 591 ( 21 equ; 0 cnn)
% Maximal formula atoms : 65 ( 5 avg)
% Number of connectives : 2024 ( 186 ~; 274 |; 96 &;1413 @)
% ( 0 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 10 con; 0-3 aty)
% Number of variables : 252 ( 46 ^; 179 !; 27 ?; 252 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
reg: $tType ).
thf(decl_38,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(decl_50,type,
mvalid: ( $i > $o ) > $o ).
thf(decl_54,type,
c: reg > reg > $o ).
thf(decl_56,type,
p: reg > reg > $o ).
thf(decl_58,type,
o: reg > reg > $o ).
thf(decl_60,type,
ec: reg > reg > $o ).
thf(decl_61,type,
pp: reg > reg > $o ).
thf(decl_62,type,
tpp: reg > reg > $o ).
thf(decl_63,type,
ntpp: reg > reg > $o ).
thf(decl_64,type,
catalunya: reg ).
thf(decl_65,type,
france: reg ).
thf(decl_66,type,
spain: reg ).
thf(decl_67,type,
paris: reg ).
thf(decl_68,type,
a: $i > $i > $o ).
thf(decl_70,type,
esk1_0: $i ).
thf(decl_71,type,
esk2_0: $i ).
thf(decl_72,type,
esk3_1: reg > reg ).
thf(decl_73,type,
esk4_1: reg > reg ).
thf(decl_74,type,
esk5_1: reg > reg ).
thf(decl_75,type,
esk6_1: reg > reg ).
thf(decl_76,type,
esk7_0: reg ).
thf(decl_77,type,
esk8_1: reg > reg ).
thf(decl_78,type,
esk9_1: reg > reg ).
thf(decl_81,type,
esk12_0: reg ).
thf(decl_82,type,
esk13_0: reg ).
thf(decl_83,type,
esk14_1: reg > reg ).
thf(decl_84,type,
esk15_1: reg > reg ).
thf(decl_85,type,
esk16_1: reg > reg ).
thf(decl_86,type,
esk17_1: reg > reg ).
thf(o,axiom,
( o
= ( ^ [X28: reg,X29: reg] :
? [X25: reg] :
( ( p @ X25 @ X28 )
& ( p @ X25 @ X29 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',o) ).
thf(p,axiom,
( p
= ( ^ [X23: reg,X24: reg] :
! [X25: reg] :
( ( c @ X25 @ X23 )
=> ( c @ X25 @ X24 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',p) ).
thf(pp,axiom,
( pp
= ( ^ [X34: reg,X35: reg] :
( ( p @ X34 @ X35 )
& ~ ( p @ X35 @ X34 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',pp) ).
thf(ec,axiom,
( ec
= ( ^ [X32: reg,X33: reg] :
( ( c @ X32 @ X33 )
& ~ ( o @ X32 @ X33 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',ec) ).
thf(con,conjecture,
( mvalid
@ ( mbox @ a
@ ^ [X44: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',con) ).
thf(mbox,axiom,
( mbox
= ( ^ [X13: $i > $i > $o,X6: $i > $o,X3: $i] :
! [X14: $i] :
( ~ ( X13 @ X3 @ X14 )
| ( X6 @ X14 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',mbox) ).
thf(mvalid,axiom,
( mvalid
= ( ^ [X6: $i > $o] :
! [X3: $i] : ( X6 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',mvalid) ).
thf(ntpp,axiom,
( ntpp
= ( ^ [X38: reg,X39: reg] :
( ( pp @ X38 @ X39 )
& ~ ? [X25: reg] :
( ( ec @ X25 @ X38 )
& ( ec @ X25 @ X39 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',ntpp) ).
thf(ax3,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X43: $i] : ( ntpp @ paris @ france ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',ax3) ).
thf(tpp,axiom,
( tpp
= ( ^ [X36: reg,X37: reg] :
( ( pp @ X36 @ X37 )
& ? [X25: reg] :
( ( ec @ X25 @ X36 )
& ( ec @ X25 @ X37 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',tpp) ).
thf(ax1,axiom,
( mvalid
@ ( mbox @ a
@ ^ [X41: $i] : ( tpp @ catalunya @ spain ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',ax1) ).
thf(c_symmetric,axiom,
! [X19: reg,X20: reg] :
( ( c @ X19 @ X20 )
=> ( c @ X20 @ X19 ) ),
file('/export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p',c_symmetric) ).
thf(c_0_12,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X48: reg] :
( ( c @ X48 @ X25 )
=> ( c @ X48 @ Z0 ) )
& ! [X49: reg] :
( ( c @ X49 @ X25 )
=> ( c @ X49 @ Z1 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[o]) ).
thf(c_0_13,plain,
( p
= ( ^ [Z0: reg,Z1: reg] :
! [X25: reg] :
( ( c @ X25 @ Z0 )
=> ( c @ X25 @ Z1 ) ) ) ),
inference(fof_simplification,[status(thm)],[p]) ).
thf(c_0_14,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X53: reg] :
( ( c @ X53 @ Z0 )
=> ( c @ X53 @ Z1 ) )
& ~ ! [X54: reg] :
( ( c @ X54 @ Z1 )
=> ( c @ X54 @ Z0 ) ) ) ) ),
inference(fof_simplification,[status(thm)],[pp]) ).
thf(c_0_15,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X50: reg] :
( ! [X51: reg] :
( ( c @ X51 @ X50 )
=> ( c @ X51 @ Z0 ) )
& ! [X52: reg] :
( ( c @ X52 @ X50 )
=> ( c @ X52 @ Z1 ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ec]) ).
thf(c_0_16,plain,
( o
= ( ^ [Z0: reg,Z1: reg] :
? [X25: reg] :
( ! [X48: reg] :
( ( c @ X48 @ X25 )
=> ( c @ X48 @ Z0 ) )
& ! [X49: reg] :
( ( c @ X49 @ X25 )
=> ( c @ X49 @ Z1 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_12,c_0_13]) ).
thf(c_0_17,negated_conjecture,
~ ( mvalid
@ ( mbox @ a
@ ^ [X44: $i] :
( ( o @ catalunya @ spain )
& ( o @ france @ paris ) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
thf(c_0_18,plain,
( mbox
= ( ^ [Z0: $i > $i > $o,Z1: $i > $o,Z2: $i] :
! [X14: $i] :
( ~ ( Z0 @ Z2 @ X14 )
| ( Z1 @ X14 ) ) ) ),
inference(fof_simplification,[status(thm)],[mbox]) ).
thf(c_0_19,plain,
( mvalid
= ( ^ [Z0: $i > $o] :
! [X3: $i] : ( Z0 @ X3 ) ) ),
inference(fof_simplification,[status(thm)],[mvalid]) ).
thf(c_0_20,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X63: reg] :
( ( c @ X63 @ Z0 )
=> ( c @ X63 @ Z1 ) )
& ~ ! [X64: reg] :
( ( c @ X64 @ Z1 )
=> ( c @ X64 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X65: reg] :
( ! [X66: reg] :
( ( c @ X66 @ X65 )
=> ( c @ X66 @ X25 ) )
& ! [X67: reg] :
( ( c @ X67 @ X65 )
=> ( c @ X67 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X68: reg] :
( ! [X69: reg] :
( ( c @ X69 @ X68 )
=> ( c @ X69 @ X25 ) )
& ! [X70: reg] :
( ( c @ X70 @ X68 )
=> ( c @ X70 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[ntpp]) ).
thf(c_0_21,plain,
( pp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X53: reg] :
( ( c @ X53 @ Z0 )
=> ( c @ X53 @ Z1 ) )
& ~ ! [X54: reg] :
( ( c @ X54 @ Z1 )
=> ( c @ X54 @ Z0 ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_14,c_0_13]) ).
thf(c_0_22,plain,
( ec
= ( ^ [Z0: reg,Z1: reg] :
( ( c @ Z0 @ Z1 )
& ~ ? [X50: reg] :
( ! [X51: reg] :
( ( c @ X51 @ X50 )
=> ( c @ X51 @ Z0 ) )
& ! [X52: reg] :
( ( c @ X52 @ X50 )
=> ( c @ X52 @ Z1 ) ) ) ) ) ),
inference(apply_def,[status(thm)],[c_0_15,c_0_16]) ).
thf(c_0_23,negated_conjecture,
~ ! [X78: $i,X77: $i] :
( ~ ( a @ X78 @ X77 )
| ( ? [X71: reg] :
( ! [X72: reg] :
( ( c @ X72 @ X71 )
=> ( c @ X72 @ catalunya ) )
& ! [X73: reg] :
( ( c @ X73 @ X71 )
=> ( c @ X73 @ spain ) ) )
& ? [X74: reg] :
( ! [X75: reg] :
( ( c @ X75 @ X74 )
=> ( c @ X75 @ france ) )
& ! [X76: reg] :
( ( c @ X76 @ X74 )
=> ( c @ X76 @ paris ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_17]),c_0_16]),c_0_18]),c_0_19])]) ).
thf(c_0_24,plain,
( ntpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X63: reg] :
( ( c @ X63 @ Z0 )
=> ( c @ X63 @ Z1 ) )
& ~ ! [X64: reg] :
( ( c @ X64 @ Z1 )
=> ( c @ X64 @ Z0 ) )
& ~ ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X65: reg] :
( ! [X66: reg] :
( ( c @ X66 @ X65 )
=> ( c @ X66 @ X25 ) )
& ! [X67: reg] :
( ( c @ X67 @ X65 )
=> ( c @ X67 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X68: reg] :
( ! [X69: reg] :
( ( c @ X69 @ X68 )
=> ( c @ X69 @ X25 ) )
& ! [X70: reg] :
( ( c @ X70 @ X68 )
=> ( c @ X70 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
thf(c_0_25,negated_conjecture,
! [X120: reg,X123: reg] :
( ( a @ esk1_0 @ esk2_0 )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ( c @ ( esk3_1 @ X120 ) @ X120 ) )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ( c @ ( esk4_1 @ X120 ) @ X120 )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ( c @ ( esk5_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) )
& ( ( c @ ( esk6_1 @ X123 ) @ X123 )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) )
& ( ~ ( c @ ( esk6_1 @ X123 ) @ paris )
| ~ ( c @ ( esk5_1 @ X123 ) @ france )
| ~ ( c @ ( esk4_1 @ X120 ) @ spain )
| ~ ( c @ ( esk3_1 @ X120 ) @ catalunya ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])])]) ).
thf(c_0_26,plain,
! [X89: $i,X88: $i] :
( ~ ( a @ X89 @ X88 )
| ( ! [X79: reg] :
( ( c @ X79 @ paris )
=> ( c @ X79 @ france ) )
& ~ ! [X80: reg] :
( ( c @ X80 @ france )
=> ( c @ X80 @ paris ) )
& ~ ? [X81: reg] :
( ( c @ X81 @ paris )
& ~ ? [X82: reg] :
( ! [X83: reg] :
( ( c @ X83 @ X82 )
=> ( c @ X83 @ X81 ) )
& ! [X84: reg] :
( ( c @ X84 @ X82 )
=> ( c @ X84 @ paris ) ) )
& ( c @ X81 @ france )
& ~ ? [X85: reg] :
( ! [X86: reg] :
( ( c @ X86 @ X85 )
=> ( c @ X86 @ X81 ) )
& ! [X87: reg] :
( ( c @ X87 @ X85 )
=> ( c @ X87 @ france ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax3]),c_0_24]),c_0_18]),c_0_19])]) ).
thf(c_0_27,negated_conjecture,
! [X19: reg,X18: reg] :
( ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X19 ) @ X19 )
| ( c @ ( esk3_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_28,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X19 ) @ X19 )
| ( c @ ( esk3_1 @ X19 ) @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_29,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X55: reg] :
( ( c @ X55 @ Z0 )
=> ( c @ X55 @ Z1 ) )
& ~ ! [X56: reg] :
( ( c @ X56 @ Z1 )
=> ( c @ X56 @ Z0 ) )
& ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X57: reg] :
( ! [X58: reg] :
( ( c @ X58 @ X57 )
=> ( c @ X58 @ X25 ) )
& ! [X59: reg] :
( ( c @ X59 @ X57 )
=> ( c @ X59 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X60: reg] :
( ! [X61: reg] :
( ( c @ X61 @ X60 )
=> ( c @ X61 @ X25 ) )
& ! [X62: reg] :
( ( c @ X62 @ X60 )
=> ( c @ X62 @ Z1 ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[tpp]) ).
thf(c_0_30,plain,
! [X126: $i,X127: $i,X128: reg,X130: reg,X132: reg,X133: reg,X135: reg,X136: reg] :
( ( ~ ( c @ X128 @ paris )
| ( c @ X128 @ france )
| ~ ( a @ X126 @ X127 ) )
& ( ( c @ esk7_0 @ france )
| ~ ( a @ X126 @ X127 ) )
& ( ~ ( c @ esk7_0 @ paris )
| ~ ( a @ X126 @ X127 ) )
& ( ~ ( c @ X135 @ ( esk9_1 @ X130 ) )
| ( c @ X135 @ X130 )
| ~ ( c @ X130 @ france )
| ~ ( c @ X132 @ ( esk8_1 @ X130 ) )
| ( c @ X132 @ X130 )
| ~ ( c @ X130 @ paris )
| ~ ( a @ X126 @ X127 ) )
& ( ~ ( c @ X136 @ ( esk9_1 @ X130 ) )
| ( c @ X136 @ france )
| ~ ( c @ X130 @ france )
| ~ ( c @ X132 @ ( esk8_1 @ X130 ) )
| ( c @ X132 @ X130 )
| ~ ( c @ X130 @ paris )
| ~ ( a @ X126 @ X127 ) )
& ( ~ ( c @ X135 @ ( esk9_1 @ X130 ) )
| ( c @ X135 @ X130 )
| ~ ( c @ X130 @ france )
| ~ ( c @ X133 @ ( esk8_1 @ X130 ) )
| ( c @ X133 @ paris )
| ~ ( c @ X130 @ paris )
| ~ ( a @ X126 @ X127 ) )
& ( ~ ( c @ X136 @ ( esk9_1 @ X130 ) )
| ( c @ X136 @ france )
| ~ ( c @ X130 @ france )
| ~ ( c @ X133 @ ( esk8_1 @ X130 ) )
| ( c @ X133 @ paris )
| ~ ( c @ X130 @ paris )
| ~ ( a @ X126 @ X127 ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])])]) ).
thf(c_0_31,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk5_1 @ paris ) @ paris )
| ( c @ ( esk3_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X18 ) @ X18 )
| ( c @ ( esk3_1 @ X19 ) @ X19 )
| ( c @ ( esk4_1 @ X19 ) @ X19 ) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
thf(c_0_32,plain,
( tpp
= ( ^ [Z0: reg,Z1: reg] :
( ! [X55: reg] :
( ( c @ X55 @ Z0 )
=> ( c @ X55 @ Z1 ) )
& ~ ! [X56: reg] :
( ( c @ X56 @ Z1 )
=> ( c @ X56 @ Z0 ) )
& ? [X25: reg] :
( ( c @ X25 @ Z0 )
& ~ ? [X57: reg] :
( ! [X58: reg] :
( ( c @ X58 @ X57 )
=> ( c @ X58 @ X25 ) )
& ! [X59: reg] :
( ( c @ X59 @ X57 )
=> ( c @ X59 @ Z0 ) ) )
& ( c @ X25 @ Z1 )
& ~ ? [X60: reg] :
( ! [X61: reg] :
( ( c @ X61 @ X60 )
=> ( c @ X61 @ X25 ) )
& ! [X62: reg] :
( ( c @ X62 @ X60 )
=> ( c @ X62 @ Z1 ) ) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_29,c_0_21]),c_0_22]) ).
thf(c_0_33,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ france )
| ~ ( c @ X18 @ paris )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
thf(c_0_34,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk5_1 @ paris ) @ paris )
| ( c @ ( esk4_1 @ X18 ) @ X18 )
| ( c @ ( esk3_1 @ X18 ) @ X18 ) ),
inference(ef,[status(thm)],[c_0_31]) ).
thf(c_0_35,plain,
! [X105: $i,X104: $i] :
( ~ ( a @ X105 @ X104 )
| ( ! [X95: reg] :
( ( c @ X95 @ catalunya )
=> ( c @ X95 @ spain ) )
& ~ ! [X96: reg] :
( ( c @ X96 @ spain )
=> ( c @ X96 @ catalunya ) )
& ? [X97: reg] :
( ( c @ X97 @ catalunya )
& ~ ? [X98: reg] :
( ! [X99: reg] :
( ( c @ X99 @ X98 )
=> ( c @ X99 @ X97 ) )
& ! [X100: reg] :
( ( c @ X100 @ X98 )
=> ( c @ X100 @ catalunya ) ) )
& ( c @ X97 @ spain )
& ~ ? [X101: reg] :
( ! [X102: reg] :
( ( c @ X102 @ X101 )
=> ( c @ X102 @ X97 ) )
& ! [X103: reg] :
( ( c @ X103 @ X101 )
=> ( c @ X103 @ spain ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[ax1]),c_0_32]),c_0_18]),c_0_19])]) ).
thf(c_0_36,plain,
! [X158: reg,X159: reg] :
( ~ ( c @ X158 @ X159 )
| ( c @ X159 @ X158 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_symmetric])]) ).
thf(c_0_37,negated_conjecture,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ ( esk5_1 @ paris ) @ france )
| ( c @ ( esk3_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
thf(c_0_38,negated_conjecture,
a @ esk1_0 @ esk2_0,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_39,plain,
! [X142: $i,X143: $i,X144: reg,X147: reg,X150: reg] :
( ( ~ ( c @ X144 @ catalunya )
| ( c @ X144 @ spain )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ esk12_0 @ spain )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ esk12_0 @ catalunya )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ esk13_0 @ catalunya )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk15_1 @ X147 ) @ X147 )
| ( c @ ( esk14_1 @ X147 ) @ X147 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk15_1 @ X147 ) @ catalunya )
| ( c @ ( esk14_1 @ X147 ) @ X147 )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk15_1 @ X147 ) @ X147 )
| ~ ( c @ ( esk14_1 @ X147 ) @ esk13_0 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk15_1 @ X147 ) @ catalunya )
| ~ ( c @ ( esk14_1 @ X147 ) @ esk13_0 )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ esk13_0 @ spain )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk17_1 @ X150 ) @ X150 )
| ( c @ ( esk16_1 @ X150 ) @ X150 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk17_1 @ X150 ) @ spain )
| ( c @ ( esk16_1 @ X150 ) @ X150 )
| ~ ( a @ X142 @ X143 ) )
& ( ( c @ ( esk17_1 @ X150 ) @ X150 )
| ~ ( c @ ( esk16_1 @ X150 ) @ esk13_0 )
| ~ ( a @ X142 @ X143 ) )
& ( ~ ( c @ ( esk17_1 @ X150 ) @ spain )
| ~ ( c @ ( esk16_1 @ X150 ) @ esk13_0 )
| ~ ( a @ X142 @ X143 ) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])])]) ).
thf(c_0_40,plain,
! [X18: reg,X19: reg] :
( ( c @ X19 @ X18 )
| ~ ( c @ X18 @ X19 ) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
thf(c_0_41,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk5_1 @ paris ) @ france )
| ( c @ ( esk4_1 @ X18 ) @ X18 )
| ( c @ ( esk3_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
thf(c_0_42,plain,
! [X18: reg,X3: $i,X14: $i] :
( ( c @ X18 @ spain )
| ~ ( c @ X18 @ catalunya )
| ~ ( a @ X3 @ X14 ) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
thf(c_0_43,negated_conjecture,
! [X18: reg] :
( ( c @ france @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
thf(c_0_44,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ france @ ( esk5_1 @ paris ) )
| ( c @ ( esk4_1 @ catalunya ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
thf(c_0_45,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk3_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_46,negated_conjecture,
( ( c @ ( esk4_1 @ catalunya ) @ spain )
| ( c @ france @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_44,c_0_38]) ).
thf(c_0_47,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk3_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_48,negated_conjecture,
! [X18: reg] :
( ( c @ france @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
thf(c_0_49,negated_conjecture,
! [X18: reg] :
( ( c @ france @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk6_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_46]) ).
thf(c_0_50,negated_conjecture,
( ( c @ ( esk5_1 @ paris ) @ paris )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ france @ ( esk5_1 @ paris ) ) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
thf(c_0_51,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ paris ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_50]),c_0_40]) ).
thf(c_0_52,negated_conjecture,
! [X19: reg,X18: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X19 ) @ X19 )
| ( c @ ( esk3_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_53,negated_conjecture,
( ( c @ ( esk5_1 @ paris ) @ france )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_51,c_0_38]) ).
thf(c_0_54,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk6_1 @ paris ) @ paris )
| ( c @ ( esk3_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
thf(c_0_55,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk4_1 @ X18 ) @ X18 )
| ( c @ ( esk3_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_54]) ).
thf(c_0_56,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk4_1 @ catalunya ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_55]) ).
thf(c_0_57,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk3_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_58,negated_conjecture,
( ( c @ ( esk4_1 @ catalunya ) @ spain )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk6_1 @ paris ) ) ),
inference(spm,[status(thm)],[c_0_56,c_0_38]) ).
thf(c_0_59,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ( c @ ( esk3_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_60,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
thf(c_0_61,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk6_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(spm,[status(thm)],[c_0_59,c_0_58]) ).
thf(c_0_62,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_63,negated_conjecture,
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk6_1 @ paris ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_53]) ).
thf(c_0_64,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk6_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
thf(c_0_65,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_66,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ X18 @ ( esk6_1 @ X18 ) ) ),
inference(spm,[status(thm)],[c_0_40,c_0_64]) ).
thf(c_0_67,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ ( esk6_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(spm,[status(thm)],[c_0_65,c_0_63]) ).
thf(c_0_68,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ paris ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_66]) ).
thf(c_0_69,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ X18 @ ( esk6_1 @ X18 ) )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
thf(c_0_70,negated_conjecture,
( ( c @ ( esk5_1 @ paris ) @ france )
| ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk6_1 @ paris ) ) ),
inference(spm,[status(thm)],[c_0_68,c_0_38]) ).
thf(c_0_71,negated_conjecture,
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk4_1 @ catalunya ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
thf(c_0_72,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk4_1 @ catalunya ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_71]) ).
thf(c_0_73,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk5_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_74,negated_conjecture,
( ( c @ ( esk4_1 @ catalunya ) @ spain )
| ( c @ paris @ ( esk6_1 @ paris ) ) ),
inference(spm,[status(thm)],[c_0_72,c_0_38]) ).
thf(c_0_75,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_76,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_63]) ).
thf(c_0_77,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk6_1 @ X18 ) @ X18 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_74]),c_0_63]) ).
thf(c_0_78,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_79,negated_conjecture,
( ( c @ ( esk5_1 @ paris ) @ paris )
| ( c @ paris @ ( esk6_1 @ paris ) ) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
thf(c_0_80,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk6_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_74]),c_0_63]) ).
thf(c_0_81,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ ( esk5_1 @ paris ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_79]) ).
thf(c_0_82,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
thf(c_0_83,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk6_1 @ paris ) )
| ( c @ X18 @ ( esk6_1 @ X18 ) )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(spm,[status(thm)],[c_0_40,c_0_80]) ).
thf(c_0_84,negated_conjecture,
( ( c @ ( esk5_1 @ paris ) @ france )
| ( c @ paris @ ( esk6_1 @ paris ) ) ),
inference(spm,[status(thm)],[c_0_81,c_0_38]) ).
thf(c_0_85,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk5_1 @ paris ) )
| ( c @ ( esk4_1 @ catalunya ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_82]) ).
thf(c_0_86,negated_conjecture,
c @ paris @ ( esk6_1 @ paris ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
thf(c_0_87,negated_conjecture,
( ( c @ ( esk4_1 @ catalunya ) @ spain )
| ( c @ paris @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_85,c_0_38]) ).
thf(c_0_88,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_89,negated_conjecture,
c @ ( esk6_1 @ paris ) @ paris,
inference(spm,[status(thm)],[c_0_40,c_0_86]) ).
thf(c_0_90,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(spm,[status(thm)],[c_0_45,c_0_87]) ).
thf(c_0_91,negated_conjecture,
! [X18: reg] :
( ( c @ paris @ ( esk5_1 @ paris ) )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ X18 ) @ X18 )
| ( c @ ( esk6_1 @ X18 ) @ X18 ) ),
inference(spm,[status(thm)],[c_0_47,c_0_87]) ).
thf(c_0_92,negated_conjecture,
! [X19: reg,X18: reg] :
( ( c @ ( esk4_1 @ X19 ) @ X19 )
| ( c @ ( esk3_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_93,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk5_1 @ paris ) @ paris )
| ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk3_1 @ X18 ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
thf(c_0_94,negated_conjecture,
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ paris @ ( esk5_1 @ paris ) ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_40]) ).
thf(c_0_95,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk3_1 @ X18 ) @ X18 )
| ( c @ ( esk4_1 @ X18 ) @ X18 ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_89]),c_0_41]) ).
thf(c_0_96,negated_conjecture,
( ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ paris ) @ paris ) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_40]) ).
thf(c_0_97,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk4_1 @ catalunya ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_95]) ).
thf(c_0_98,negated_conjecture,
! [X18: reg,X19: reg] :
( ( c @ ( esk4_1 @ X19 ) @ X19 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_99,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ ( esk5_1 @ paris ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_96]) ).
thf(c_0_100,negated_conjecture,
( ( c @ ( esk4_1 @ catalunya ) @ spain )
| ( c @ ( esk3_1 @ catalunya ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_97,c_0_38]) ).
thf(c_0_101,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ paris ) @ france )
| ~ ( c @ ( esk3_1 @ X18 ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_98,c_0_89]) ).
thf(c_0_102,negated_conjecture,
( ( c @ ( esk5_1 @ paris ) @ france )
| ( c @ ( esk4_1 @ catalunya ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_99,c_0_38]) ).
thf(c_0_103,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(spm,[status(thm)],[c_0_57,c_0_100]) ).
thf(c_0_104,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk3_1 @ catalunya ) @ catalunya )
| ( c @ ( esk6_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(spm,[status(thm)],[c_0_59,c_0_100]) ).
thf(c_0_105,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk4_1 @ catalunya ) @ catalunya )
| ( c @ ( esk4_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk3_1 @ X18 ) @ catalunya ) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
thf(c_0_106,negated_conjecture,
c @ ( esk3_1 @ catalunya ) @ catalunya,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_53]) ).
thf(c_0_107,negated_conjecture,
c @ ( esk4_1 @ catalunya ) @ catalunya,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
thf(c_0_108,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk4_1 @ catalunya ) @ spain )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_42,c_0_107]) ).
thf(c_0_109,negated_conjecture,
c @ ( esk4_1 @ catalunya ) @ spain,
inference(spm,[status(thm)],[c_0_108,c_0_38]) ).
thf(c_0_110,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk5_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_109]),c_0_106])]) ).
thf(c_0_111,negated_conjecture,
c @ ( esk5_1 @ paris ) @ paris,
inference(spm,[status(thm)],[c_0_110,c_0_89]) ).
thf(c_0_112,negated_conjecture,
! [X18: reg,X19: reg] :
( ~ ( c @ ( esk6_1 @ X18 ) @ paris )
| ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk4_1 @ X19 ) @ spain )
| ~ ( c @ ( esk3_1 @ X19 ) @ catalunya ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
thf(c_0_113,negated_conjecture,
! [X3: $i,X14: $i] :
( ( c @ ( esk5_1 @ paris ) @ france )
| ~ ( a @ X3 @ X14 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_111]) ).
thf(c_0_114,negated_conjecture,
! [X18: reg] :
( ~ ( c @ ( esk5_1 @ X18 ) @ france )
| ~ ( c @ ( esk6_1 @ X18 ) @ paris ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_109]),c_0_106])]) ).
thf(c_0_115,negated_conjecture,
! [X18: reg] :
( ( c @ ( esk6_1 @ X18 ) @ X18 )
| ~ ( c @ ( esk5_1 @ X18 ) @ france ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_109]),c_0_106])]) ).
thf(c_0_116,negated_conjecture,
c @ ( esk5_1 @ paris ) @ france,
inference(spm,[status(thm)],[c_0_113,c_0_38]) ).
thf(c_0_117,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG006^1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n016.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 18:38:49 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.6E9ikVthjJ/E---3.1_740049.p
% 2.77/0.71 % Version: 3.5.1-ho
% 2.77/0.71 % Preprocessing class: HSMSSMSSMLLNHSN.
% 2.77/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.77/0.71 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 2.77/0.71 % Starting post_as_ho3 with 300s (1) cores
% 2.77/0.71 % Starting new_ho_12 with 300s (1) cores
% 2.77/0.71 % Starting new_bool_2 with 300s (1) cores
% 2.77/0.71 % new_bool_2 with pid 740079 completed with status 0
% 2.77/0.71 % Result found by new_bool_2
% 2.77/0.71 % Preprocessing class: HSMSSMSSMLLNHSN.
% 2.77/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.77/0.71 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 2.77/0.71 % Starting post_as_ho3 with 300s (1) cores
% 2.77/0.71 % Starting new_ho_12 with 300s (1) cores
% 2.77/0.71 % Starting new_bool_2 with 300s (1) cores
% 2.77/0.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.77/0.71 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.77/0.71 % Search class: HGHNF-FFMF21-SHSSMSBN
% 2.77/0.71 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 2.77/0.71 % Starting SubtermCWHack with 28s (1) cores
% 2.77/0.71 % SubtermCWHack with pid 740089 completed with status 0
% 2.77/0.71 % Result found by SubtermCWHack
% 2.77/0.71 % Preprocessing class: HSMSSMSSMLLNHSN.
% 2.77/0.71 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.77/0.71 % Starting new_ho_10_cnf2 with 1500s (5) cores
% 2.77/0.71 % Starting post_as_ho3 with 300s (1) cores
% 2.77/0.71 % Starting new_ho_12 with 300s (1) cores
% 2.77/0.71 % Starting new_bool_2 with 300s (1) cores
% 2.77/0.71 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 2.77/0.71 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 2.77/0.71 % Search class: HGHNF-FFMF21-SHSSMSBN
% 2.77/0.71 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 2.77/0.71 % Starting SubtermCWHack with 28s (1) cores
% 2.77/0.71 % Preprocessing time : 0.002 s
% 2.77/0.71
% 2.77/0.71 % Proof found!
% 2.77/0.71 % SZS status Theorem
% 2.77/0.71 % SZS output start CNFRefutation
% See solution above
% 2.77/0.71 % Parsed axioms : 98
% 2.77/0.71 % Removed by relevancy pruning/SinE : 77
% 2.77/0.71 % Initial clauses : 50
% 2.77/0.71 % Removed in clause preprocessing : 0
% 2.77/0.71 % Initial clauses in saturation : 50
% 2.77/0.71 % Processed clauses : 1181
% 2.77/0.71 % ...of these trivial : 12
% 2.77/0.71 % ...subsumed : 369
% 2.77/0.71 % ...remaining for further processing : 800
% 2.77/0.71 % Other redundant clauses eliminated : 0
% 2.77/0.71 % Clauses deleted for lack of memory : 0
% 2.77/0.71 % Backward-subsumed : 400
% 2.77/0.71 % Backward-rewritten : 140
% 2.77/0.71 % Generated clauses : 11873
% 2.77/0.71 % ...of the previous two non-redundant : 11734
% 2.77/0.71 % ...aggressively subsumed : 0
% 2.77/0.71 % Contextual simplify-reflections : 28
% 2.77/0.71 % Paramodulations : 11755
% 2.77/0.71 % Factorizations : 118
% 2.77/0.71 % NegExts : 0
% 2.77/0.71 % Equation resolutions : 0
% 2.77/0.71 % Disequality decompositions : 0
% 2.77/0.71 % Total rewrite steps : 281
% 2.77/0.71 % ...of those cached : 212
% 2.77/0.71 % Propositional unsat checks : 0
% 2.77/0.71 % Propositional check models : 0
% 2.77/0.71 % Propositional check unsatisfiable : 0
% 2.77/0.71 % Propositional clauses : 0
% 2.77/0.71 % Propositional clauses after purity: 0
% 2.77/0.71 % Propositional unsat core size : 0
% 2.77/0.71 % Propositional preprocessing time : 0.000
% 2.77/0.71 % Propositional encoding time : 0.000
% 2.77/0.71 % Propositional solver time : 0.000
% 2.77/0.71 % Success case prop preproc time : 0.000
% 2.77/0.71 % Success case prop encoding time : 0.000
% 2.77/0.71 % Success case prop solver time : 0.000
% 2.77/0.71 % Current number of processed clauses : 260
% 2.77/0.71 % Positive orientable unit clauses : 62
% 2.77/0.71 % Positive unorientable unit clauses: 0
% 2.77/0.71 % Negative unit clauses : 2
% 2.77/0.71 % Non-unit-clauses : 196
% 2.77/0.71 % Current number of unprocessed clauses: 10441
% 2.77/0.71 % ...number of literals in the above : 65536
% 2.77/0.71 % Current number of archived formulas : 0
% 2.77/0.71 % Current number of archived clauses : 540
% 2.77/0.71 % Clause-clause subsumption calls (NU) : 114477
% 2.77/0.71 % Rec. Clause-clause subsumption calls : 33230
% 2.77/0.71 % Non-unit clause-clause subsumptions : 728
% 2.77/0.71 % Unit Clause-clause subsumption calls : 2040
% 2.77/0.71 % Rewrite failures with RHS unbound : 0
% 2.77/0.71 % BW rewrite match attempts : 37
% 2.77/0.71 % BW rewrite match successes : 35
% 2.77/0.71 % Condensation attempts : 0
% 2.77/0.71 % Condensation successes : 0
% 2.77/0.71 % Termbank termtop insertions : 285784
% 2.77/0.71 % Search garbage collected termcells : 1851
% 2.77/0.71
% 2.77/0.71 % -------------------------------------------------
% 2.77/0.71 % User time : 0.433 s
% 2.77/0.71 % System time : 0.020 s
% 2.77/0.71 % Total time : 0.453 s
% 2.77/0.71 % Maximum resident set size: 3992 pages
% 2.77/0.71
% 2.77/0.71 % -------------------------------------------------
% 2.77/0.71 % User time : 0.435 s
% 2.77/0.71 % System time : 0.025 s
% 2.77/0.71 % Total time : 0.460 s
% 2.77/0.71 % Maximum resident set size: 5120 pages
% 2.77/0.71 % E exiting
%------------------------------------------------------------------------------